Sparse Seismic Deconvolution by Method of Orthogonal Matching Pursuit

An improved orthogonal matching pursuit method for denoising high-frequency ultrasonic detection signals of flip chips

Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

In this paper, a novel sparse convex representation learning algorithm is proposed for estimating the intrinsic dimension of a dataset. Caratheodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset of P consisting of d + 1 or fewer points such that x lies in the convex hull of P'. We believe that the maximum value, among the numbers of the nonzero elements of the sparsest convex representation of all points, implies the intrinsic dimension of a data set. The sparsest convex representation of a point lying in a convex hull means that it is a convex combination of the minimum number of the extreme points. Based on this basic idea, we constructed an objective function. Moreover, an improved orthogonal matching pursuit (OMP) method is proposed for solving it to derive a sparse convex representation. The obtained solutions can be used for estimating the dimension of the data set. The experiment results show the effectiveness and efficiency of our proposed method.

In this paper, joint compressed sensing (CS)-based estimation of transmit power, geographical location and frequency bands of active primary users (PUs) using three reconstruction algorithms, orthogonal matching pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and iterative hard thresholding (IHT) methods is investigated. In the first simulations, the performances of OMP, CoSaMP and IHT methods are evaluated in different signal to noise ratios (SNRs) and different values of sparsity. The first experiment demonstrates that OMP is the high performance reconstruction algorithm but it needs a bit higher complexity. Moreover, two scenarios for decision-making is considered in fusion center (FC) and respected simulation results for two cases, ideal and non-ideal lossy channels between secondary users (SUs) and fusion center, are represented. Second experiments show that decision-making based on integrated reconstruction is more efficient than averaging on three separate reconstructions in both ideal and lossy channels.

Pseudo-inverses of difference matrices and their application to sparse signal approximation

ABSTRACTThe biggest challenge of the traditional 3D orthogonal matching pursuit (OMP) method for direction-of-departure (DOD), direction-of-arrival (DOA) and Doppler frequency estimation in bistatic multiple-input multiple-output (MIMO) radar is the heavy computational burden due to a large number of atoms in the overcomplete dictionary. In this paper, low complexity 3D-OMP algorithms are investigated. First, the traditional 3D-OMP algorithm is given. Then, two-dimensionality reduced OMP-based algorithms are proposed exploiting the property of Khatri-Rao product and proper sparse representation. Also, the multiple measurement vectors (MMV) model is introduced to our OMP algorithms to guarantee the estimation performance. The simulation results show that the DOD, DOA and Doppler frequency can be effectively estimated with a small number of pulses and low computation cost. With similar accuracy compared with the traditional 3D-OMP method, much lower computational burden can be achieved by using the proposed methods.

Compressed Sensing (CS) has been considered a very effective means of reducing energy consumption at the energy-constrained wireless body sensor networks for monitoring the multi-lead Electrocardiogram (MECG) signals. This paper develops the compressed sensing theory for sparse modeling and effective multi-channel ECG compression. A basis matrix with Gaussian kernels is proposed to obtain the sparse representation of each channel, which showed the closest similarity to the ECG signals. Thereafter, the greedy orthogonal matching pursuit (OMP) method is used to obtain the sparse representation of the signals. After obtaining the sparse representation of each ECG signal, the compressed sensing theory could be used to compress the signals as much as possible. Following the compression, the compressed signal is reconstructed utilizing the greedy orthogonal matching pursuit (OMP) optimization technique to demonstrate the accuracy and reliability of the algorithm. Moreover, as the wavelet basis matrix is another sparsifying basis to sparse representations of ECG signals, the compressed sensing is applied to the ECG signals using the wavelet basis matrix. The simulation results indicated that the proposed algorithm with Gaussian basis matrix reduces the reconstruction error and increases the compression ratio.

We present a blind user identification method for the direct-sequence code division multiple access (DS-CDMA) signal from a sparse signal representation perspective using an overcomplete basis composed of all possible spreading sequences. The main idea of the proposed algorithm is to combine the sparsity characteristic of the DS-CDMA signal in terms of spreading sequences with the autocorrelation and the cross-correlation characteristics of spreading sequences. Firstly, the DS-CDMA signal samples are cut into several temporal windows. Each signal of the temporal window is corresponding to a measurement of the active user's spreading sequence. Secondly, the overcomplete dictionary of spreading sequences is constructed according to the structure of spreading sequence and the support coefficient of its every atom is calculated by performing the Orthogonal Matching Pursuit (OMP) method on samples of all temporal windows. Finally, with the help of the minimum description length (MDL) criterion, the number of active users is estimated and then the spreading sequences of active users are identified by inspecting their support coefficients. Simulation results demonstrate that our proposed method is effective for both synchronous short-code (SC) DS-CDMA signal and long-code (LC) DS-CDMA signal, even with many active users and low SNR.

In this paper, we present improved performance compressed sensing (CS) based pulse Doppler radar. CS is an emerging sampling technique which uses very few number of samples to reconstruct original signal. Improvement in performance is achieved using Orthogonal Matching Pursuit (OMP) method with Fourier dictionary at low signal to noise ratio (SNR). OMP is an iterative and fast reconstruction method while Fourier dictionary is used to transform the original signal from time domain to Fourier domain. A significant reduction of sampling frequency by a factor of 360 is achieved at SNR as low as 10 dB, while preserving essential signal information. Low signal reconstruction error leads to good detection performance using Generalized Likelihood Ratio Test (GLRT), a detector based on ratio of probabilities of detection and false alarm. Simulation results demonstrate usefulness of the ideas presented.

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

The theory of compressed sensing (or compressive sampling, CS for short) indicates if a signal is sparse or compressible in a certain transform domain, the transformed higher-dimensional signal can be projected onto a lower-dimensional space by a measurement matrix, which is uncorrelated with the transform basis, and then the signal can be accurately reconstructed by solving the convex optimization problem in accordance with a small amount of measured values. The algorithm proposed in this paper combines compressed sensing theory with wavelet packet analysis, which first decomposes the original image with the wavelet packet to make it sparse, and then retains the low-frequency coefficients in line with the optimal basis of the wavelet packet, meanwhile, makes random measurements of all the high-frequency coefficients according to the compressed sensing theory, and last restores them with the orthogonal matching pursuit (OMP) method, and does the inverse transform of the wavelet packet to reconstruct the original image, to achieve the image compression. The simulation results demonstrate this algorithm of simpleness and high efficiency, with the better reconstructed image quality, is superior to the other two image compression algorithms also based on the compressed sensing theory.

Sparse representation provides an efficient way for the compression of hyperspectral images in the literature. In this work, an improved version of the Spectral-Spatial Adaptive Sparse Representation (SSASR), Modified SSASR (MSSASR), is proposed for hyperspectral image compression. In the first step of the proposed method, superpixel maps are generated for adaptive spatio-spectral representation. Then, the best possible dictionary is computed for the representation of the data. Afterwards, sparse coefficients are determined depending on the dictionary by Simultaneous Orthogonal Matching Pursuit (SOMP) method. In the final step, the dictionary and sparse coefficients are encoded by quantization and entropy encoding. This paper has the following novelties: modified dictionary learning step, new ordering scheme and Differential Pulse Code Modulation (DPCM) usage. Owing to modified dictionary learning, the sparse coefficients can be represented more compact than traditional SSASR. By using of new ordering scheme, it is not needed to send the superpixel map as side information. Moreover, DCPM usage lowers the magnitudes of sparse coefficients. Thanks to these modifications, the proposed method achieves an important improvement on compression performance. In the experimental results, the proposed method is compared with PCA+JPEG2000, DWT+JPEG2000, 3D-SPECK, 3D-TARP and SSASR methods on Indian Pines, Washington DC Mall, Jasper Ridge and Moffett Field scenes. The evaluation is carried out not only using distance and similarity metrics, namely, signal-to-noise ratio, mean spectral angle and mean spectral correlation metrics but also computation times. Additionally, reconstruction quality in anomaly regions is also used for comparison. Experimental results show that the proposed method outperforms the other compression methods in terms of quality metrics and anomaly preserving performance.

The process of gathering of scientific data plays an important role in telemonitoring and communications technologies of underwater information. However, to obtain such a huge data in underwater-wireless-sensor-networks, conventional methods often fail in energy efficiency. Compressive sampling (CS) provides a new perspective to solve the problem. Unfortunately, the underwater acoustic signal is non-sparse in the time domain and the current CS methods cannot be used directly. This paper adopts the discrete cosine transform-based dictionary-matrix for sparse representation. In addition, the measurement matrix is optimized via the steepest descent method for more efficient sampling. Then, we introduce an approach based on an approximated l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm at the receiving terminal, to search the sparse solution via the steepest descent method and projections. Combing with the measurement matrix and dictionary-matrix, the sparse estimation is used for reconstruction. Experimental results confirm the superior performances of the strategies of the proposed compressive sampling and reconstruction than those of the traditional measurement matrix and reconstruction methods, including matching pursuit and orthogonal matching pursuit methods.

A highly secure oblivious sparse coding-based watermarking system for ownership verification